| Title | Wavelet Time-Frequency Analysis and Its Applications to Water Waves – Wavelet Characterizations and the Optimum Basis(2/2) |
| Dept | Transportation Technology and Information Division |
| Year | 2004 |
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| Summary | Published in May 2004 IOT SERIAL No. 93-79-7112, 148pp. Comprehensive categories of discrete wavelets are studied first. The relevant characterizations and various intrinsic properties are extensively illustrated. Physical counterparts of analytical aspects are provided when possible. The entropy criteria are applied to the whole set of wavelets for signals obtained from wave-tank experiments, and the optimal wavelet basis is identified to be the semi-orthogonal cardinal spline dual wavelet. Besides, each individual wavelet's pertinence to the applications of water-wave-related signals is linked to the phase distribution of a wavelet characteristic function. That is to say, we identified the analytical essence of the statistical behaviors of the entropy results. Based on the identified discrete best basis, a second optimization is applied, and this is done through incorporating the advantages related to the continuous wavelet transform. And this in turn points to the counterpart continuous wavelet. Furthermore, for the better modeling of real physics, a third optimization is also implemented through the adaptation of wavelet time-frequency windows. With these results, the author firmly believes that if you ever find an individual wavelet you have great chance to assign it into one of the categories covered here and if not, you have great reason to conceive that its properties must fall within (or between) the covered characterizations and thus, in water wave applications, any wavelet's fate or possible usefulness is decreed accordingly - overall, it is really hard to beat the optimum basis and the methodology given in this study. |
| Post date | 2005/08/15 |
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